Homework 2

Part I

Ch4.5 Occupational Mobility

library("tidyverse")
library("grid")
library("gridExtra")
library("scales")
library("GGally")

data(Yamaguchi87, package="vcdExtra")
Yamaguchi87 <- tbl_df(Yamaguchi87)

grid_arrange_shared_legend <- function(..., ncol = length(list(...)), nrow = 1, position = c("bottom", "right")) {
  plots <- list(...)
  position <- match.arg(position)
  g <- ggplotGrob(plots[[1]] + theme(legend.position = position))$grobs
  legend <- g[[which(sapply(g, function(x) x$name) == "guide-box")]]
  lheight <- sum(legend$height)
  lwidth <- sum(legend$width)
  gl <- lapply(plots, function(x) x + theme(legend.position="none"))
  gl <- c(gl, ncol = ncol, nrow = nrow)
  combined <- switch(position,
                     "bottom" = arrangeGrob(do.call(arrangeGrob, gl),
                                            legend,
                                            ncol = 1,
                                            heights = unit.c(unit(1, "npc") - lheight, lheight)),
                     "right" = arrangeGrob(do.call(arrangeGrob, gl),
                                           legend,
                                           ncol = 2,
                                           widths = unit.c(unit(1, "npc") - lwidth, lwidth)))
  grid.newpage()
  grid.draw(combined)
}

p45a <- Yamaguchi87 %>% 
  select(Country, Son, Freq) %>% 
  group_by(Country, Son) %>% 
  summarise(Freq = sum(Freq)) %>% 
  mutate(Percentage=Freq/sum(Freq)) %>% 
  mutate(Occupation=Son) %>% 
  ggplot(aes(x=Occupation, y=Percentage, fill=Occupation)) +
  geom_bar(stat="identity") +
  facet_grid(. ~ Country) +
  ggtitle("(a) Distributions of Sons' Occupations in Three Countries") + 
  xlab("") + ylab("") +
  scale_y_continuous(labels=percent) +
  scale_fill_brewer(palette="RdPu") +
  theme_linedraw()
p45b <- Yamaguchi87 %>% 
  filter(Country=="UK") %>% 
  select(-Country) %>% 
  gather(Generation, Occupation, -Freq) %>% 
  group_by(Generation, Occupation) %>% 
  summarise(Freq = sum(Freq)) %>% 
  mutate(Percentage=Freq/sum(Freq)) %>% 
  mutate(Occupation=factor(Occupation, levels = c("UpNM", "LoNM", "UpM", "LoM", "Farm"))) %>% 
  ggplot(aes(x=Occupation, y=Percentage, fill=Occupation)) +
  geom_bar(stat="identity") +
  facet_grid(. ~ Generation) +
  ggtitle("(b) Distributions of Fathers' and Sons' occupations in UK") + 
  xlab("") + ylab("") +
  scale_y_continuous(labels=percent) +
  scale_fill_brewer(palette="RdPu") +
  theme_linedraw() 
grid_arrange_shared_legend(p45a, p45b, ncol = 1, nrow = 2)

1. US and UK have similar distribution of occupations, however Japan is different. We can see the bars of occupations in Japan are almost same height.

2. The distributions of Father and Son in UK look similar, but there are more Up Mon-Manual and less Low Manual and Farm in Son.

3. The results are what I would have expected. Data of these three countries were derived from surveys in early 1970s. At that time, UK and US are more developed and industrialized than Japan, so they have more people work in non-agriculture area as what we see in Figure (a). With the growth of economy and technology, machines replaced more and more human workers, so the percentage of people who work in farm and low manual area decresed and the percentage of people working in non-manual area increased, which match what we see in Figure (b).

---

Ch4.6 Whisky

data(Scotch, package="bayesm")
Scotch <- tbl_df(Scotch)

Scotch %>% 
  gather(Brand, Count) %>% 
  filter(Brand!='Other.Brands') %>%
  group_by(Brand) %>% 
  summarise(Consumption = sum(Count)) %>% 
  ggplot(aes(x=reorder(Brand, Consumption), y=Consumption, fill=Consumption)) +
  geom_bar(stat="identity") + 
  coord_flip() +
  xlab("Brand") +
  ggtitle("(a) Consumption per Brand I") + 
  scale_fill_gradient(low="blue", high="red") +
  theme_linedraw() 

1. Graph (a) represents the amount of consumption in decrease order. Chivas.Regal is the best brand based on the information we have.

2. Since there’s an obvious gap between Glenfiddich and Pinch..Haig. on the graph and the number of consumption for these two are 334 and 117, I would pick a number in between, let’s say 200 as the cutoff for big brand.

data(whiskey, package="flexmix")
w1 <- tbl_df(data.frame(whiskey$Incidence * whiskey$Freq)) %>% 
  gather(Brand, Count) %>% 
  group_by(Brand) %>% 
  summarise(Consumption = sum(Count))
w2 <- tbl_df(whiskey_brands) %>% 
  mutate(Brand=gsub("([^a-zA-Z])", ".", Brand))
    
whiskey_all <- left_join(w1, w2, by=c("Brand" = "Brand"))

whiskey_all %>% 
  filter(Brand!='Other.brands') %>% 
  ggplot(aes(x=Consumption, y=reorder(Brand, Consumption))) +
  geom_segment(aes(yend=Brand), xend=0, color='grey50') + 
  geom_point(size=3, aes(color=Bottled)) + 
  facet_grid(Type ~ ., scales='free_y', space='free_y') +
  ylab("Brand") +
  ggtitle("(c) Consumption per Brand II") + 
  scale_color_manual(values = c("royalblue1", "violetred1")) +
  theme_linedraw()

4. By coloring different Bottled category, we see that most Brands come outside of United States, so I think “whisky” is better.

---

Ch5.8 Olive oils from Italy

data(olives, package="extracat")
olives <- tbl_df(olives)

olives %>%
  ggpairs(columns=3:10,
          lower=list(continuous=wrap("points", alpha=0.3, size=0.1, color="royalblue1")), 
          diag=list(continuous=wrap("densityDiag", alpha=0.7, size=0.2), axisLabels='none'), 
          upper=list(continuous=wrap("cor", size=rel(3), color="violetred1"))
          ) +
  theme_linedraw() +
  theme(
    text=element_text(size = 7),
    axis.text=element_text(size = 6), 
    axis.text.x=element_text(angle = 60))

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1. From the plot above we can tell that Palmitoleic and Palmitic are strongly positively associated. Oleic and Palmitic, Oleic and Palmitoleic are strongly negatively associated.

2. Yes. All the scatter plots of Eicosenoic associated with others have many outliers locate at the bottom, like a line.

---

Ch5.10 Hertzsprung-Russell

data("HRstars", package="GDAdata")
HRstars <- tbl_df(HRstars)

HRstars %>% 
  mutate(AM = V+5*(1+log10(Para))) %>% 
  ggplot(aes(x=BV, y=AM, color=BV)) +
  geom_point(alpha=.3, size=.5) +
  scale_color_gradient(low="blue", high="red") +
  xlab("Color (BV)") + ylab("Absolute Maganitude (AM)") +
  scale_y_reverse() +
  theme_linedraw() 

1. Comparing to the graph from Wikipedia, the patterns are similar. Graph drawn from HRstars data clearly shows White Dwarfs, Main Sequence and Giants. But it is probabaly due to the small amount of data we have, it is not as clear as the one on Wikipedia, and lacks of details.

2. It seems like the graph from Wiki has more data for Giants, so the shape of Giants is a longer line.

3. I colored points by BV. And in the graph, there is a very obvious trend that more blue points have been drawn on the left and more red on the right.

---

Ch6.5 Bodyfat

data(bodyfat, package="MMST")
bodyfat <- tbl_df(bodyfat)

bodyfat %>% 
  ggparcoord(alphaLines=0.2, scale="uniminmax", groupColumn="age") +
  xlab("") + ylab("") +
  # scale_color_gradient(low="blue", high="red") +
  theme_linedraw() +
  theme(axis.text.x=element_text(angle = 15))

1. Yes, there are outliers. Individual outliers can be seen on most of the variables (weight, neck, chest, abdomen, hip, thign, knee, ankle and biceps) and usually are extreme high values.

2. Height has many small subgroups and positive correlation with weight and neck.

3. density and bodyfat are strongly negative correlated.

4. Yes. Because if we put the first two variables far away from each other, it will be impossible to see the negative correlation. The new graph made after reordering does a better job in showing correlations.

bodyfat %>% 
  ggparcoord(alphaLines=0.2, scale="uniminmax",
             order=c(7,15,6,2,11,3,10,1,4,5,9,13,12,14,8), 
             groupColumn="age") +
  xlab("") + ylab("") +
  # scale_colour_manual(values = c("#00BFC4")) +
  theme_linedraw() +
  theme(axis.text.x=element_text(angle = 15))

---

Ch6.7 Wine

data(wine, package="MMST")
wine_mmst <- tbl_df(wine)
data(wine, package="pgmm")
wine_pgmm <- tbl_df(wine)
wine_pgmm <- wine_pgmm %>% 
  mutate_all(funs(as.numeric)) %>% 
  mutate_at(vars(Type), funs(as.factor))
wine_classname <- wine_mmst %>% 
  select(Class=class, classdigit) %>% 
  distinct()
wine_all <- left_join(wine_pgmm, wine_classname, by=c("Type" = "classdigit"))

wine_all %>% 
  ggparcoord(columns=2:28, groupColumn="Class", alphaLines=0.2, scale="uniminmax", order="anyClass") +
  xlab("") + ylab("") +
  coord_flip() +
  scale_colour_manual(values = c("royalblue1", "black", "violetred1")) +
  # scale_color_brewer(palette="Dark2") +
  theme_linedraw()

1. In the pcp graph, we can see that there are evidences which several variables can be used to seperate classes. Flavanoids seems to be able to separate all three clases. Proline, OD280/OD315 of Diluted Wines, OD280/OD315 of Flavanoids, Hue, Alcohol maybe helpful to separate one class from the other two.

2. Yes, there are outliers. Many variables have extreme value of the rightside in the pcp graph, such as Flavanoids, hue, Chloride and Calcium.

wine_all %>% 
  ggparcoord(columns=2:28, alphaLines=0.2, scale="uniminmax", groupColumn="Class") +
  xlab("") + ylab("") +
  ggtitle("") + 
  facet_grid(~Class) +
  coord_flip() +
  scale_colour_manual(values = c("royalblue1", "black", "violetred1")) +
  theme_linedraw() + 
  theme(panel.spacing.x=unit(0.8, "lines"))

3. We deduces several variables in each Class which have subgroups from the pcp graph: Color Intensity in class Barbera, Malic Acid in class Barolo and Total Phenols in class Grignolino

---

Part II

Yamaguchi87 Dataset

Yamaguchi87 %>% 
  gather(Generation, Occupation, -Freq, -Country) %>% 
  group_by(Country, Generation, Occupation) %>% 
  summarise(Freq = sum(Freq)) %>% 
  spread(Generation, Freq) %>% 
  mutate(Diff = Son - Father) %>% 
  mutate(PercentageDiff=Diff/sum(Father + Son)) %>% 
  mutate(Occupation=factor(Occupation, levels = c("UpNM", "LoNM", "UpM", "LoM", "Farm"))) %>% 
  ggplot(aes(x=Occupation, y=PercentageDiff, fill=PercentageDiff)) +
  geom_bar(stat="identity") +
  facet_grid(. ~ Country) +
  xlab("") + ylab("") +
  scale_y_continuous(labels=percent) +
  scale_fill_gradient(low="blue", high="red") +
  theme_linedraw() 

The y axis of this bar chart is the difference of Freq between Father and Son in percentage, positive number means more people for variable Father, negative number means the opposite. The x axis represents the occupations. There is a general trend for all these three regions which is the percetage of people who work in more tranditional areas reduces and the percetage of people who work in more “advanced”, or say non-manual areas increases for Son compare to Father. The change of occupation structure reflects the developments in economy and technology at 60s and early 70s.

---

Olives Dataset

olives %>%
  ggpairs(columns=3:10, 
          lower=list(continuous=wrap("points", alpha=0.3, size=0.1)), 
          diag=list(continuous=wrap("densityDiag", alpha=0.7, size=0.1), axisLabels='none'), 
          upper=list(continuous=wrap("cor", size=1.8)),
          ggplot2::aes(colour=Region)
          ) +
  theme_linedraw() +
  theme(
    text=element_text(size = 7),
    axis.text=element_text(size = 6), 
    axis.text.x=element_text(angle = 30))

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After coloring olives data by region, the evidences of difference pattern among regions show up. The most obvious one is in the last row, which represents eicosenoic on x-axis, all red and green points (region North and Sardinia) locate at the bottom of y-axis like a line, however the blue points (South) have total different pattern. Actually not only for this one feature, most of the features have distinct pattern in each region. Parallel coordinate plot is one good way to show such differences.

olives %>% 
  ggparcoord(columns=3:10, alphaLines=0.2, scale="uniminmax", groupColumn="Region") +
  xlab("") + ylab("") +
  ggtitle("") + 
  facet_grid(Region ~.) +
  # coord_flip() +
  scale_colour_manual(values = c("royalblue1", "black", "violetred1")) +
  theme_linedraw() + 
  theme(panel.spacing.x=unit(0.8, "lines"))

glimpse(olives)

Observations: 572
Variables: 11
$ Area          <fctr> North-Apulia, North-Apulia, North-Apulia, North-Apulia, North-Apulia, ...
$ Region        <fctr> South, South, South, South, South, South, South, South, South, South, ...
$ palmitic      <int> 1088, 911, 966, 1051, 911, 1100, 1082, 1037, 1051, 1074, 875, 943, 1278...
$ palmitoleic   <int> 73, 54, 57, 67, 49, 61, 60, 55, 35, 70, 52, 94, 69, 70, 77, 67, 53, 39,...
$ stearic       <int> 224, 246, 240, 259, 268, 235, 239, 213, 219, 214, 243, 183, 205, 195, 2...
$ oleic         <int> 7709, 8113, 7952, 7771, 7924, 7728, 7745, 7944, 7978, 7728, 8018, 7840,...
$ linoleic      <int> 781, 549, 619, 672, 678, 734, 709, 633, 605, 747, 655, 788, 957, 742, 7...
$ linolenic     <int> 31, 31, 50, 50, 51, 39, 46, 26, 21, 50, 41, 42, 45, 46, 43, 56, 54, 42,...
$ arachidic     <int> 61, 63, 78, 80, 70, 64, 83, 52, 65, 79, 79, 75, 70, 75, 78, 83, 89, 74,...
$ eicosenoic    <int> 29, 29, 35, 46, 44, 35, 33, 30, 24, 33, 32, 31, 28, 30, 33, 45, 51, 26,...
$ Test.Training <fctr> Training, Training, Training, Training, Training, Training, Training, ...

p1 <- olives %>%
  select(-Area, -Region, -Test.Training) %>% 
  ggcorr(label = TRUE, label_size = 2, label_round = 2, label_alpha = TRUE, low = "royalblue1", mid = "#EEEEEE", high = "violetred1", hjust = 0.75, size=2, legend.position="None") +
  ggtitle("All Regions")
p2 <- olives %>%
  filter(Region=="North") %>% 
  select(-Area, -Region, -Test.Training) %>% 
  ggcorr(label = TRUE, label_size = 2, label_round = 2, label_alpha = TRUE, low = "royalblue1", mid = "#EEEEEE", high = "violetred1", hjust = 0.75, size=2, legend.position="None") +
  ggtitle("North")
p3 <- olives %>%
  filter(Region=="Sardinia") %>% 
  select(-Area, -Region, -Test.Training) %>% 
  ggcorr(label = TRUE, label_size = 2, label_round = 2, label_alpha = TRUE, low = "royalblue1", mid = "#EEEEEE", high = "violetred1", hjust = 0.75, size=2, legend.position="None") +
  ggtitle("Sardinia")
p4 <- olives %>%
  filter(Region=="South") %>% 
  select(-Area, -Region, -Test.Training) %>% 
  ggcorr(label = TRUE, label_size = 2, label_round = 2, label_alpha = TRUE, low = "royalblue1", mid = "#EEEEEE", high = "violetred1", hjust = 0.75, size=2, legend.position="None") +
  ggtitle("South")
grid.arrange(p1,p2,p3,p4)

Furthermore, I noticed that not all the combination of variables has linear relations and I presented the evidence by showing the actual value of correlation and highlighting with color and alpha.